7.2 Soundness and validity: a taste of logic 259
Commentary
The answer is that the argument is not sound,
but it is valid. Make no mistake about this.
What makes it valid is that if its premises had
both been true, there would have been no
escaping the truth of the conclusion. For no
large, genuine diamond would have so low a
value, and this ring, according to the friend,
has practically none. If the second claim were
as true as the first, then the stone could not
have been a diamond.
Of course we know, from the story, that
the conclusion is false. But that doesn’t make
the argument invalid. Its form, when we cut
it down to the bare bones, is the same as
that of [9]:If (d) the stone was a diamond,
then (v) the ring would be valuable.The ring is not valuable (Not-v).The stone is not a diamond (Not-d).What practical use is the assessment of an
argument’s validity, if we already know the
premises are false? As far as judging its
soundness, none at all. It would be unsound
even if it were valid. No argument can be
considered sound if it is based on a lie, as this
one is. But if we are giving a critical evaluation
of an argument, we must be able to say why it
is unsound; and it would be incorrect to say
that this is invalid. What the above example
also shows is that valid reasoning can be
abused and exploited for persuasive purposes.
It is partly because [12] is valid that it looks
and sounds plausible. Andrea is persuaded,
dishonestly, to part with a precious possession
for a fraction of its value.
The validity or otherwise of an argument is
also important if we do not know the truth or
falsity of the premises. To see this, look at the
next example. It is about a ring, too, but this
time one that evidently does have a high value.
The question is: why does it have a high value?show the difference between a valid and an
invalid form of argument, so as to make them
easier to recognise when we are interpreting
more authentic, natural arguments.
Critical thinking is directed towards real, live
arguments that you come across in newspapers,
magazines, blogs, scientific theories, political
debates and so on. The purpose of analysing
live arguments is to try to reveal their
underlying logical form as plainly as possible,
without the frills of natural language, so as to
judge whether or not the reasoning is sound –
and if not, why not. Sometimes formal logic can
assist in this (though not always).
The next argument is still a made-up example,
but it is expressed in a more natural style of
language, and a more realistic context. Suppose
someone – we’ll call her Andrea – has inherited a
ring with a large stone in it which she has reason
to think is a diamond. What is more, she is right in
her belief; but not being an expert, she has no way
of knowing for sure. A friend – some friend! –
offers to have it valued for her. He returns with
the surprising and disappointing news that the
ring is practically worthless, and that therefore the
stone is not a diamond:
[12] ‘Let’s face it: if a stone that big was a
real diamond, this ring of yours would
be worth thousands of dollars. Sadly,
it’s not worth $20. It’s pretty, but that
doesn’t make it valuable. So I’m afraid
the stone is not a diamond, and I’m
sorry to be the one who has to tell you.’He volunteers to buy it from her for his
daughter for $50, which now seems like a
generous offer. Having accepted his argument,
and its conclusion, she accepts the offer too,
and sells him the ring.
Activity
Discuss whether the argument is valid and/
or sound.